Background information

The natural-law argument states that because there are consistent and predictable natural laws in the universe, there must be a law-giver who set those laws in motion. That law-giver is assumed to be God.

Argument

Syllogism

p1. There are natural laws which govern the universe

p2. All laws have a law giver

c1. That law giver is God

Counter arguments

False premise p1: Natural laws

This argument relies on equivocation between two meanings of the word "law".

Legislative laws, such as "Do not murder" or "No littering" are prescriptive: they are established to demarcate acceptable and unacceptable behavior. If a person breaks such a law, he or she has committed a crime, and may be subject to punishment.

Natural laws, on the other hand, are descriptive: they are human concepts that describe how some aspect of the universe behaves. For instance, Newton's law of motion "F=ma" describes how solid objects behave when acted upon by a force. If a person or object breaks a physical law, then it is the law that is in error, since it obviously does not adequately describe what it seeks to describe. However, there are natural laws that are at odds with one another and are still taken to be true because there is a clear and consistent pattern. For example, entities governed by the laws of quantum mechanics do not follow the same thermodynamic laws that govern the macro universe.

"We now find that a great many things we thought were Natural Laws are really human conventions. You know that even in the remotest depth of stellar space there are still three feet to a yard. That is, no doubt, a very remarkable fact, but you would hardly call it a law of nature."

This is peripherally related to the Transcendental argument for god, in that it heavily confuses a conceptual abstraction with concrete reality.

False premise p2: The law giver

The laws in question are descriptive abstractions of what the universe does, not prescriptive legislations about what the universe can do. As such they do not require a law giver, but as long as a law giver is being asserted, it opens up the question of where god got his laws. This opens up a paradox somewhat similar to the euthyphro dilemma.

"Why did God issue just those natural laws and no others? If you say that he did it simply from his own good pleasure, and without any reason, you then find that there is something which is not subject to law, and so your train of natural law is interrupted. If you say, as more orthodox theologians do, that in all the laws which God issues he had a reason for giving those laws rather than others -- the reason, of course, being to create the best universe, although you would never think it to look at it -- if there was a reason for the laws which God gave, then God himself was subject to law, and therefore you do not get any advantage by introducing God as an intermediary."

Special Pleading c1: Which god?

Even if we grant the false premises that there are prescriptive natural laws, and by extension the existence of a lawgiver god, it does not follow that that god is the one the apologist has in mind, or even that there is only one god involved. It could just as likely be the Flying Spaghetti Monster, purple space pixies, Santa Claus, or invisible pink unicorns, as it could be Yahweh.

Invalid Argument

As the counter argument Special Pleading c1: which god? points out, the law giver could be any god and therefore even if the premises were true the conclusion could still be false. This means that the argument is invalid since the conclusion is not a valid inference from the premises. Therefore the argument is not sound.